Details Page for 0.3072

Complete Solution is Known:

MSV File: q-0.3072.msv

Growth Pattern:

(Click on a heap to see details)

Details for Q₈₂(0.3072):

Q = <a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s | a²=1, b¹⁷=b¹⁵, b²c=ab⁴, c²=b⁴, b²d=ab⁶, cd=b⁶, d²=b⁸, b²e=b⁷, ce=ab⁷, de=ab⁹, e²=b¹⁰, b²f=ab⁷, ef=abdf, f²=b¹⁰, b²g=bcf, cg=abcf, dg=ab¹⁰, eg=b¹¹, fg=ab¹¹, g²=b¹², b³h=abdf, ch=ab²h, dh=b¹¹, eh=ab¹², fh=b¹², gh=ab¹³, h²=b¹⁴, b⁵i=b¹³, ci=ab²i, di=ab⁴i, ei=b¹³, fi=ab¹³, gi=b¹⁴, hi=ab¹⁵, i²=b¹⁶, b⁶j=ab¹⁵, cj=ab²j, dj=ab⁴j, ej=b⁵j, fj=ab⁵j, gj=ab¹⁵, hj=b¹⁶, ij=ab¹⁵, j²=b¹⁶, b⁷k=b¹⁵, ck=ab²k, dk=ab⁴k, ek=b⁵k, fk=ab⁵k, gk=b⁶k, hk=ab¹⁵, ik=b¹⁶, jk=ab¹⁵, k²=b¹⁶, b⁶l=ab⁵k, cl=ab²l, dl=ab⁴l, el=b⁵l, fl=ab⁵l, gl=ab⁵k, hl=b⁶k, il=ab¹⁵, jl=b¹⁶, kl=ab¹⁵, l²=b¹⁶, b⁵m=ab⁴l, cm=ab²m, dm=ab⁴m, em=ab⁴l, fm=b⁴l, gm=ab⁵l, hm=ab⁵k, im=b⁶k, jm=ab¹⁵, km=b¹⁶, lm=ab¹⁵, m²=b¹⁶, b⁴n=ab³m, cn=ab²n, dn=b³m, en=ab⁴m, fn=b⁴m, gn=b⁴l, hn=ab⁵l, in=ab⁵k, jn=b⁶k, kn=ab¹⁵, ln=b¹⁶, mn=ab¹⁵, n²=b¹⁶, b³o=ab²n, co=ab²o, do=b³n, eo=b³m, fo=ab³m, go=b⁴m, ho=b⁴l, io=ab⁵l, jo=ab⁵k, ko=b⁶k, lo=ab¹⁵, mo=b¹⁶, no=ab¹⁵, o²=b¹⁶, b²p=abo, cp=bo, dp=ab²n, ep=b³n, fp=ab³n, gp=ab³m, hp=b⁴m, ip=b⁴l, jp=ab⁵l, kp=ab⁵k, lp=b⁶k, mp=ab¹⁵, np=b¹⁶, op=ab¹⁵, p²=b¹⁶, bq=ap, cq=bp, dq=ab²o, eq=ab²n, fq=b²n, gq=ab³n, hq=ab³m, iq=b⁴m, jq=b⁴l, kq=ab⁵l, lq=ab⁵k, mq=b⁶k, nq=ab¹⁵, oq=b¹⁶, pq=ab¹⁵, q²=b¹⁶, br=aq, cr=ap, dr=bo, er=ab²o, fr=b²o, gr=b²n, hr=ab³n, ir=ab³m, jr=b⁴m, kr=b⁴l, lr=ab⁵l, mr=ab⁵k, nr=b⁶k, or=ab¹⁵, pr=b¹⁶, qr=ab¹⁵, r²=b¹⁶, bs=ar, cs=aq, ds=bp, es=bo, fs=abo, gs=b²o, hs=b²n, is=ab³n, js=ab³m, ks=b⁴m, ls=b⁴l, ms=ab⁵l, ns=ab⁵k, os=b⁶k, ps=ab¹⁵, qs=b¹⁶, rs=ab¹⁵, s²=b¹⁶>

P = {a, b², b⁴, b⁶, b⁸, b¹⁰, b¹², b¹⁴, b¹⁶, ae, bf, abg, h, b²h, abi, ab³i, j, b²j, b⁴j, abk, ab³k, ab⁵k, l, b²l, b⁴l, abm, ab³m, n, b²n, abo, p, r}

Phi = 1 a 1 a 1 b ab b ab a 1 a 1 b ab b ab c ac c b² abc bc abc ab³ d ad d b⁴ e ae e f abe g abe b⁶ bg h bg ab⁷ bh i bh b⁸ bi j bi ab⁹ bj k bj b¹⁰ bk l bk ab¹¹ bl m bl b¹² bm n bm ab¹³ bn o bn b¹⁴ bo p bo ab¹⁵ bp q bp b¹⁶ ap r ap ab¹⁵ aq s aq b¹⁶ ar

Monoid Structure